Preliminary Material

This chapter gives some preliminary material on number theory and algebraic geometry. Section 1 gives basic preliminary notation, both mathematical and logistical. Section 2 describes what algebraic geometry is assumed of the reader, and gives a few conventions that will be assumed here. Section 3 gives a few more details on the field of definition of a variety. Section 4 does the same as Section 2 for number theory. The remaining sections of this chapter give slightly longer descriptions of some topics in algebraic geometry that will be needed: Kodaira’s lemma in Section 5, and descent in Section 6.